A long-distance telephone call costs $1.80 for the first 3 minutes and $0.40 for each additional minutes. If the charge for an x-minutes long distance call at this rate was $4.20, then x=

Options

A. `7`
B. `8`
C. `9`
D. `10`

Answer

To solve the problem step by step, we need to set up an equation based on the information given about the cost of the long-distance call.

### Step 1: Understand the cost structure
The cost for the first 3 minutes of the call is $1.80. For any additional minutes beyond the first 3 minutes, the cost is $0.40 per minute.

### Step 2: Set up the equation
Let \( x \) be the total duration of the call in minutes. If the call lasts longer than 3 minutes, then the additional minutes are \( x - 3 \). The total cost of the call can be expressed as:

\[ \text{Total Cost} = \text{Cost for first 3 minutes} + \text{Cost for additional minutes} \]

This can be written mathematically as:

\[ 4.20 = 1.80 + 0.40(x - 3) \]

### Step 3: Simplify the equation
Now, we will simplify the equation step by step:

1. Subtract the cost of the first 3 minutes from both sides:

\[ 4.20 - 1.80 = 0.40(x - 3) \]

This simplifies to:

\[ 2.40 = 0.40(x - 3) \]

### Step 4: Solve for \( x - 3 \)
Next, we will isolate \( x - 3 \) by dividing both sides by 0.40:

\[ x - 3 = \frac{2.40}{0.40} \]

Calculating the right side gives:

\[ x - 3 = 6 \]

### Step 5: Solve for \( x \)
Now, we add 3 to both sides to find \( x \):

\[ x = 6 + 3 \]

Thus, we find:

\[ x = 9 \]

### Conclusion
The total duration of the call is \( x = 9 \) minutes.

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